Someone who has the same birthday as you. It is refered to as a shared birthday. Some may refer to it as a mutual birthday. Facebook is notorious for displaying all your friends' birthdays on your homepage to see common birthdays. When the time for the birthday comes, one friend says happy birthday to another and the other friend replies the same way. It is a known fact that people enjoy discussing common birthdays.

Guy 1: Dude, did you know Jay Leno is a birthday buddy with Jessica Alba?
Guy 2: Yea, I saw it on The Tonight Show last night.
Guy 1: Yea, they're both on April 28th.